PREDICTION OF MAXIMUM CRACK WIDTH FORMULA FOR RCC … · PREDICTION OF MAXIMUM CRACK WIDTH FORMULA FOR RCC FLEXURAL MEMBER Lakshmi T N, Jayasree S Abstract—A formula for the maximum

International Journal of Scientific & Engineering Research, Volume 7, Issue 10, October-2016 48 ISSN 2229-5518

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PREDICTION OF MAXIMUM CRACK WIDTH FORMULA FOR RCC FLEXURAL MEMBER

Lakshmi T N, Jayasree S

Abstract—A formula for the maximum crack width has been developed by incorporating eight governing parameters such as steel stress, grade of concrete, area of steel reinforcement, diameter of bars, % of steel reinforcement, spacing of bars, yield stress of steel reinforcement and concrete cover based on statistical analysis of the author’s test results reported in literatures using Statistical Package for Social Science (SPSS) software. An experimental investigation was also carried out on six RC beam models and compared with formula suggested in international codes such as BS 8110-1997/ IS 456-2000, ACI code 318, GBJ 10-89 1989, BS EN 1992-1-1: 2004 and ECP 203-2007. The performance of the proposed formula is checked with experimental results and it shows well correlation

Index Terms—Beam Model, Crack Width, International Codes, Predicted equation, Reinforced Concrete.

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1 INTRODUCTION

RACKwidth calculation is one of the serviceability re-quirements in the structural members. The occurrence of cracks in RC structures is unavoidable because of the low

tensile strength of concrete. Cracks form when the tensile stress in concrete exceeds its tensile strength [1]. Cracks in a RC member will always be a threat for the satisfactory per-formance and serviceability of the structure; it has significant influence on serviceability, durability, aesthetic and force transfer. Hence, an accurate estimation of the crack widths and its predictions are essential in structural design.

Limiting crack width is important, from the aesthetic point of view to ensure water tightness and to safe guard the rein-forcement against corrosion [2].RC structures designed with low steel stresses under service loads undergo very limited cracking, expect for the cracks that occur due to shrinkage of concrete and temperature changes. In many cases no cracking is visible at all because many members are not subjected to their full service load and the concrete has some tensile strength. To minimize these adverse effects, serviceability lim-it states (SLS) for RC structures are usually applied to ensure their functionality and structural integrity under service load-ing condition.Prediction of crack width has been studied by many researchers such as Gergely and Lutz, 1968 [3]; R.J Frosch, 1999 [4]; B.B Broms, 1965 [5]; Kang et al., 1987 [6];N .Ganesan, 1998 [7]. As many variables influence the crack width and spacing of RC flexural members, due to the com-plexity of the problem, a number of methods have been devel-oped in the past to determine the crack width. These methods are generally based partly on theoretical basis and partly on statistical analysis of test results. Therefore, the results pre-dicted by this formula may vary by the type of specimens and the method of loading and so on.

2 EXPERIMENTAL INVESTIGATION An experimental investigation was conducted on six RC beam specimens of size 100 x 150 x 1000 mm. The specimen details are shown in Table 1. All the beams were tested under two point loading in a Universal Testing Machine (UTM) of 1000kN capacity. A schematic representation of loading confi-guration is shown in Fig.1. The maximum crack width were measured at loads 10, 20, 30 and 40 kN using crack detection microscope of 50x magnification.

TABLE 1 SPECIMEN DETAILS

Fig. 1. Loading configuration

C

———————————————— • Lakshmi T N is currently pursuing masters degree program in structural

engineering, Mar- Baselios college of engineering and technology, Univer-sity of Kerala, India, PH-+919633972118. E-mail: [email protected]

• Jayasree S is currently working as Assistant Professor, Mar- Baselios col-lege of engineering and technology, University of Kerala, India, E-mail: [email protected]

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2.1Comparison of Crack Width with InternationalCodes The observed crack widths for all the beam models were com-pared with the formulas recommended in the British standard BS 8110 – 1997 [8], American standard ACI 318 – 1995, 05, 08 & 11 [9],[10],[11], Chinese code GBJ 10 – 1989 [12], European standard BS EN 1992 – 1 – 1: 2004 [13] and Egyptian standard ECP 203 – 2007 [14]. Its graphical representation is shown in Fig. 2 to 6. Where wtheo represents calculated crack width us-ing International codes. It was observed that the values of crack width as predicted by the ACI code and Euro code cor-related well with the experimental values.

Fig. 2. Comparison of Experimental crack width with BS 8110 code equation

Fig. 3. Comparison of Experimental crack width with ACI 318 code equation

Fig. 4. Comparison of Experimental crack width with Chinese codeequation

Fig. 5. Comparison of Experimental crack width with Euro

code equation

Fig. 6. Comparison of Experimental crack width with Egyptian code equation

3 PREDICTION OF MAXIMUM CRACK WIDTH EQUATION

A new formula for maximum crack width is predicted by in-corporating the effect of steel stress, grade of concrete, area of steel reinforcement, diameter of bars, % of steel reinforcement, spacing of bars, yield stress of steel reinforcement and con-crete cover based on statistical analysis of the author’s test results reported in literatures using SPSS software. The rele-vant data used for regression analysis are 130 beam specimen results of various authors such as Hognestad, Kaar-Mattock, C&CA, Nawy and Syed [15].

Non linear regression is the method of finding a nonlinear model of arbitrary relationship between dependent variable and a set of independent variables; it is accomplished by using iterative estimation algorithms. Here dependent variable is crack width (wcal) and fourteen independent variables are steel stress (fs), modulus of elasticity of steel (Es), number and diameter of reinforcing bar (n & φ), yield stress of steel rein-forcement (fy), grade of concrete (fck), spacing of bar (s), con-crete cover (c), beam section (b, d & d’) and percentage of steel reinforcement (μ). Parameter estimates and residual sum of squares are obtained for all iteration.

To predict the maximum crack width equation, the eight governing parameters given in heading 3 were incorporated in the statistical regression analysis along with three regression coefficients C1, C2 and C3 [16]. The regression equation takes the form,

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wcal = fsEs

[C1 (Φ/μ) + C2 ( Sf y

nfck) + C3 c] (1)

The values of C1, C2 and C3 were determined from the sta-tistical analysis and the solution for the regression coefficients led to the following equation.

wcal = fsEs

[0.03 (Φ/μ) + 0.021( Sf y

nfck) + 1.4c] (2)

Where,

wcal = Maximum crack width in mm;

Φ = Diameter of bars in mm;

μ = Percentage steel reinforcement;

s = Spacing of bars in mm;

fy = Yield stress in N/mm2;

n = Number of bars;

fck = Grade of concrete in N/mm2;

c = Concrete cover in mm.

fs = Steel stress in N/mm2;

= m MIcr

(d – x) [7]

Icr = Moment of inertia of cracked section;

= bx3

3 + mAst (d − x)2

m = modular ratio = EsEc

Es = Modulus of elasticity for steel;

Ec = Modulus of elasticity for concrete;

M = Bending moment in Nmm;

d = Effective depth in mm;

x = Depth of neutral axis of cracked section;

Ast = Area of steel reinforcement in mm2;

b = Width of beam in mm.

SPSS provides a set of maximum crack width values cor-responding to the equation (2) by checking 130 beam specimen parameters.

3.1Modification of Predicted Equation The observed crack widths were compared with equation (2) and its graphical representation is shown in Fig.7. It was ob-served that the maximum crack width value obtained from the predicted equation for all the beam models underestimates the experimental results.

Fig. 7. Comparison of Experimental crack width with

Predicted equation Hence a correction factor is required for the equation (2) to

correlate well with the experimental values. The correction factor is obtained by plotting a graph with the ratios of expe-rimental and predicted crack width along y axis and ratios of steel stress (fs) and grade of concrete (fck) along x axis for all beam models. A best fit line was drawn in such a way that there is an equal distribution of points on either side. Slope of this line, gives the correction factor and is shown in Fig. 8.

Fig. 8. Correction Factor Graph The equation for the best fit line is,

y = 0.04x + 1 (3)

Hence the correction factor is taken as 0.04. The predicted equation is modified to the proposed equa-

tion by substituting the values of x and y in equation (3). Where,

x = fsfck

; y = wexp

wcal

wexp

wcal = [0.04 ( fs

fck) + 1] (4)

wexp = [0.04 ( fsfck

) + 1]wcal (5)

Equation (5) can be written as,

wpro = ψwcal (6)

This is the proposed Equation.

Where,

‘ψ’ = [0.04 ( fsfck

) + 1]

𝑤𝑤𝑝𝑝𝑝𝑝𝑝𝑝 = Proposed crack width in mm.

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4 COMPARISION OF PROPOSED EQUATION WITH EXPERIMENTAL RESULTS

To check the relative performance of the proposed equation, crack widths obtained from equation (6) was again compared with expe-rimental results and its graphical representation is shown in Fig. 9. It was observed that a good correlation is existing between the proposed and experimental values for all the beam models, since almost all data points lies within the limits and the scattering is acceptably small.

The mean values of the crack width ratios and the correspond-ing standard deviation, coefficient of variation for all beam models are shown in Table 2. It was observed that a good correlation exist between the proposed and experimental values for all the beam models. The proposed maximum crack width equation overesti-mate the crack width of beam models 1, 3 and 6 by 22, 20 and 4% respectively and shows a excellent correlation with the beam mod-el 5.

Fig. 9. Comparision of Proposed Equation with the Experimental crack width

TABLE 2

COMPARISON OF PROPOSED EQUATION WITH BEAM MODELS

4 CONCLUSION A new formula was proposed for the determination of maxi-mum crack width in RC flexural members incorporating the effect of steel stress, grade of concrete, area of steel reinforce-ment, diameter of bars, percentage of steel reinforcement, spacing of bars, yield stress of steel reinforcement and con-crete cover, which is not available in literatures and interna-tional code formulas.

Compared with the experimental results, the proposed eq-uation indicates well correlation. For better accuracy of the proposed equation, more and more number of test results and experimental results were required to obtain a statistically best fit equation for predicting the maximum crack width in RC flexural member, since cracking is highly random phenomena.

ACKNOWLEDGMENT The authors gratefully acknowledge the contributions of Dr. N. Ganesan, Professor and Former Dean, Department of Civil Engineering, NIT Calicut.

REFERENCES [1] N. Ganesan and K. P. Shivananda, “Comparison of international codes for

the prediction of maximum width of cracks in reinforced concrete flexural members” The Indian Concrete Journal, pp.1-7, November 1996.

[2] K. P. Shivananda, “Studies on cracking of latex modified steel fibre Rein-forced concrete flexural members” chapter 6, Journal of structural engineer-ing, pp.177-245, October 1998.

[3] M. A. Said, S. S. Mohie, G.E. Rashad and S. H. Amal, “Crack width evalua-tion for flexural RC members” Alexandria Engineering Journal, 51, pp.211–220, May 2012.

[4] R. J. Frosch “Another look at Cracking and Crack Control in Reinforced Concrete” ACI Structural Journal, pp. 437-442, June 1999.

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[5] B. Broms, “Crack width and crack spacing in reinforced concrete members”, Journal of American Concrete Institute, 62(10), pp. 1237–1256, October 1965.

[6] H. Oh and Y. J. Kang, “New formulas for maximum crack width and crack spacing in reinforced concrete flexural members” ACI Structural Journal, 84 (2), pp. 103–112, 1987.

[7] N. Ganesan, and K. P. Shivananda, “Prediction of spacing and maximum width of crack in steel fibre reinforced concrete flexural members” Journal of Structural Engineering, 24(3), pp.143-148, October 1998.

[8] Structural Use of Concrete, Part 2: Code of Practice for Special Circumstances BS 8110: Part 2: 1997, British Standard Institution, London, 1998. (CBIP), Beijing.

[9] Building Code Requirements for Reinforced Concrete, ACI 318-95 and Commentary ACI 318R-95, American Concrete Institute, Detroit, 1995.



[12] Chinese code for concrete structures GJB 10-89, 1989, Chinese building in-dustry press

[13] Euro code 2: Design of Concrete Structures – Part 1: General Rules and Rules for Buildings BS EN 1992-1-1: 2004, European Committee for Standardiza-tion, October 2004, Belgium.

[14] The Egyptian Code for Design andire Construction of Reinforced Concrete Structures, ECP 203-2007, Ministry of Housing, Egypt.

[15] G. Nawy, “Crack control in Reinforced Concrete Structure’ ACI Structural Journal, pp. 825-836, October 1968.

[16] S. H. Chowdhury and Y. C. Loo, “A New Formula for Prediction of Crack Widths in Reinforced and Partially Prestressed Concrete Beams” Advances in Structural Engineering Journal, 4(2), pp. 101-110, 2001.

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PREDICTION OF MAXIMUM CRACK WIDTH FORMULA FOR RCC … · PREDICTION OF MAXIMUM CRACK WIDTH FORMULA FOR RCC FLEXURAL MEMBER Lakshmi T N, Jayasree S Abstract—A formula for the maximum